Download Indices - PROJECT MATHS REVISION

5
3
To understand the index laws
To be able to express fractions in index form
To be able to use index laws with algebra
8
5
Introduction
2
What does 4 actually mean?
4×4
16
Introduction
5
What does 4 actually mean?
4×4×4×4×4
Introduction
How can we write 5×5×5×5
5
4
This is 5×5×5×5 written in INDEX FORM
Writing in Index Form
Write the following in Index Form
4
• 8×8×8×8
=8
6
• 3×3×3×3×3×3 = 3
3
• 9×9×9
=9
Indices
• 3x3x3x3
• 3x3x3
• 3x3
• 3
=3
4
=3
3
=3
2
=3
1
Multiplying Indices
Simplify the following leaving in index
form.
33
44
8 ×8
8
• 8
= 8×8×8 × 8×8×8×8
=8
7
Is there a quick way you can work this out?
•
33
44
8 ×8
=8
+
=8
7
Remember this only works for numbers with the
Same base number
Multiplying Indices
Simplify the following leaving in index
form.
22
44
5 ×5
5
• 5
= 5×5
× 5×5×5×5
=5
6
The Quick Way!!!
•
22
44
5 ×5
=5
+
=5
6
Remember this only works for numbers with the
Same base number
Dividing Indices
Simplify the following leaving in index
form.
2 x 2 x 2 x 2 x 2
25
55
22
=
1. 22 ÷ 22 =
2 x 2
22
=2
3
The Quick Way!!!
55
22
1. 2 ÷ 2
=2
-
=2
3
Remember this only works for numbers with the
Same base number
Indices
Simplify the following leaving in index
form.
3
3
6
3 2
This means this
2 x2
=2
1. (( 2 )
For these it is best to write them out!
Remember this only works for numbers with the
Same base number
Indices
Simplify the following leaving in index
form.
5
5
5
15
5 3
This means this
3 x3 x3 =3
1. (( 3 )
For these it is best to write them out!
Remember this only works for numbers with the
Same base number
Questions
Simplify the following numbers, leaving your answers in
index form:
1. (a) 23 x 22
25
(b) 35 x 32
37
(c)
73 x 7
74
(d) 95 x 92
97
2. (a) 23 ÷ 22
(b) 35 ÷ 32
(c)
73 ÷ 7
(d) 95 ÷ 92
2
33
72
93
Indices with Letters
• axaxaxa
• axaxa
• axa
• a
=a
4
=a
3
=a
2
=a
1
Multiplying Indices
Simplify the following leaving in index
form.
3
4
3
4
a ×a
a
• a
= a ×a ×a × a ×a × a × a
=a
7
Is there a quick way you can work this out?
•
3
3
44
a ×a
= a
+
=a
7
Remember this only works for numbers with the
Same base number
Indices with Letters
6a3 x 3a2
=
6 x a x a x a
x
3 x a x a
=
6 x 3 x a x a x a x a x a
=
18a5
The Quick Way!!!
6a3 x 3a2 =
x
x a
+
= 18a5
Indices with Letters
3a
3a5 x 2a3
=3
x
a
x
a
x
a
=
3 x 2x a
=
6a8
x
x
a
x
a
x
2
x
a
x
a
axaxaxaxaxa
Questions
Simplify the following numbers, leaving your answers in
index form:
1. (a) a3 x a2
(b) a5
a5
a6
(c)
a
a11
2. (a) (23)2
26
3
3. (a) 3b x 7b
21b
x
8
(c)
7
(b) 5b x 2b
10b8
a3
(d) a2
a4
(b) (35)2
310
5
x
14
a12
a
(73)3
79
3
x
(d) (92)5
10
9
3
3
(c) 2b x 6b (d) 2b x 15b
12b6
30b
5
2